To underscore our claims about the difficulty of calibrating the probability mass of a density model, we investigate longrun Langevin samples from normalizing flows, score models, and diffusion model. We find that the normalizing flow from the GLOW model [1]}, noise-contrastive score matching [2]} and the recovery likelihood diffusion model [3]} have misaligned steady-states as well. This shows that the problem of improper density estimation extends well beyond the EBM. In particular, the GLOW model, which is learned using end-to-end backpropagation of a fully normalized likelihood, does not learn a valid steady-state. Surprisingly, log likelihood provides no meaningful information about the steady-state of the model, as described in Appendix REF . We believe that the calibration of the model steady-state is currently best diagnosed with longrun MCMC sampling because the distribution of longrun MCMC samples represents the probability mass of the model. We hope that the observations in our work can lead to efforts to stabilize the sampling trajectories of many existing models.
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